What is $\log_{7}{2400}$ rounded to the nearest integer?
Explanation: We can have $\log_{7}343=3$ and $\log_{7}2401=4$.  Since $\log_{7}x$ increases as $x$ increases, we know that $\log_{7}343<\log_{7}2400<\log_{7}2401$, meaning $3<\log_{7}2400<4$. Moreover, we can see that $2400$ is much closer to $2401$ than to $343,$ so it stands to reason that $\log_{7}2400$ rounded to the nearest integer is $\boxed{4}.$